A meeting could take place in the coming days, with Mazzarri “intrigued” by the prospect of working in the Premier League again, according to the report.
The 55-year-old Italian was in charge of Watford in the English top flight during the 2016-17 campaign.
The former Napoli boss did a good job at Vicarage Road last season, as the Hornets escaped the drop to the Championship.
Mazzarri did a great job with Napoli between 2009 and 2013 and made the Naples outfit genuine contenders for the Scudetto.
Everton finished seventh in the Premier League last season, but Koeman’s side are struggling at the moment and could struggle to break into the top six in 2017-18.